Consistency of wavelet estimator in the multivariate multichannel deconvolution model

To estimate multivariate signals in a class of multichannel deconvolution models, this paper constructs a linear wavelet estimator by Fourier analysis, weighted summation, and wavelet projection methods. Without assuming the smoothness of unknown signal, that the wavelet estimator satisfies the mean L^p(1 \leqslant p \lt \infty ) -consistency in both regular-smooth and super-smooth cases was proved. This conclusion can help researching the convergence rates of wavelet estimator.